Counting Lattice Points on Bargraphs of Catalan Words

Toufik Mansour; José L. Ramírez; Diana A. Toquica

doi:https://doi.org/10.1007/s11786-021-00501-8

Counting Lattice Points on Bargraphs of Catalan Words

Toufik Mansour, José L. Ramírez, Diana A. Toquica

Department of Mathematics

University of Haifa

Research output: Contribution to journal › Article › peer-review

Abstract

We find formulas for the generating functions enumerating bargraphs or polyominoes associated with Catalan words according to the number of interior lattice vertices contained within and to the number of vertices of a given degree. As a consequence, one obtains simple explicit formulas for the total values of these statistics over the set of Catalan words of length n.

Original language	American English
Pages (from-to)	701-713
Number of pages	13
Journal	Mathematics in Computer Science
Volume	15
Issue number	4
DOIs	https://doi.org/10.1007/s11786-021-00501-8
State	Published - Dec 2021

Keywords

Catalan word
Generating function
Interior points
Vertex degree

All Science Journal Classification (ASJC) codes

Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

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https://doi.org/10.1007/s11786-021-00501-8

Cite this

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abstract = "We find formulas for the generating functions enumerating bargraphs or polyominoes associated with Catalan words according to the number of interior lattice vertices contained within and to the number of vertices of a given degree. As a consequence, one obtains simple explicit formulas for the total values of these statistics over the set of Catalan words of length n.",

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author = "Toufik Mansour and Ram{\'i}rez, {Jos{\'e} L.} and Toquica, {Diana A.}",

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doi = "https://doi.org/10.1007/s11786-021-00501-8",

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AU - Mansour, Toufik

AU - Ramírez, José L.

AU - Toquica, Diana A.

PY - 2021/12

Y1 - 2021/12

N2 - We find formulas for the generating functions enumerating bargraphs or polyominoes associated with Catalan words according to the number of interior lattice vertices contained within and to the number of vertices of a given degree. As a consequence, one obtains simple explicit formulas for the total values of these statistics over the set of Catalan words of length n.

AB - We find formulas for the generating functions enumerating bargraphs or polyominoes associated with Catalan words according to the number of interior lattice vertices contained within and to the number of vertices of a given degree. As a consequence, one obtains simple explicit formulas for the total values of these statistics over the set of Catalan words of length n.

KW - Catalan word

KW - Generating function

KW - Interior points

KW - Vertex degree

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DO - https://doi.org/10.1007/s11786-021-00501-8

M3 - Article

SN - 1661-8270

VL - 15

SP - 701

EP - 713

JO - Mathematics in Computer Science

JF - Mathematics in Computer Science

IS - 4

ER -

Counting Lattice Points on Bargraphs of Catalan Words

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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